Wednesday, September 28, 2011

Found Mathematics on the Playa

I've been sorting through my photos from Burning Man, and I found this set of photos of the dried playa ground. The playa is composed of a very fine particle dirt or dust that is wet mud in the winter and dry, flat earth in the late summer. As the lake bed dries, cracks are formed in the mud. The resulting cracks nicely demonstrate the idea of the self similarity of fractals in nature.

The idea is that as you zoom in, you continue to see more and more detail, and the over all shapes at every level always look the same, at least in theory.

Zoom, zoom, zoom.

Of course, this is the real world and not theoretical mathematics, so that perfect self similarity breaks down if we zoom in far enough. That reminds me of a riddle. What's the difference between theory and practice? In theory they're the same, but in practice, they're different. This is like that.

Anyway, the above photos were taking is the shade of bright daylight. Below is what the Playa looks like at night with blue and green laser lights shining on it. You can still see the cracks, but instead look at the patterns in the lights.

This pattern is quite complex since the lights are projected with more than one periodic pattern superimposed on top of one another. See how the blue forms one repeating pattern, and the larger green clusters of dots form another, but one doesn't quite match up with the other. And maybe you can even make out a repeating pattern in the smaller green dots. Pattern on top of pattern on top of pattern... This pleases me.

4 comments:

I also think I see a dominant length scale in the cracks. I can identify it in all but the greatest magnification. That is subjective, of course, so it may not be there. For example, the wave size that most people identify as dominant is close to the average of the highest third of the waves. I would bet that determining the size distribution of the pieces is a hard problem.

Does not belong here, but...I'm sorry that I have not written your name on my blog. It is very hurried and not thought of your full name. I have been corrected. Many thanks for this super good pendant,Night Sky! greetings: Szilvia (http://kaszilva.blogspot.com)